where \(\mathbf {x}\)  and \(\mathbf {x_n}\)  are the clean and partially noisy feature vectors, \(f_\theta \)  represents the encoder, \(g_\phi \)  the decoder, and \(\mathcal {L}_{\text{rec}}\)  is the reconstruction loss [1]}. It is known to be more robust than the AE, since it is designed to learn a subspace of the clean feature vectors from a noisy input, therefore learning the characteristics of the desired input.
